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Why don't objects with greater mass fall faster?

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Galileo found in his experiment that all objects regardless of its mass take same time to fall from above, if the air resistance is effectively overcome.

Aren't objects with larger mass supposed to fall quickly, since objects with larger mass attract the earth more strongly than smaller ones, and so there is stronger gravitational force between earth and objects with larger mass than between earth and objects with smaller mass?

I must be missing something.

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